Statistics Quiz #1
Subject 1, finished, 6.03 Subject 2, finished, 4.89 Subject 3, finished, 5.81 Subject 4, finished, 3.55 Subject 5, finished, 7.00 Subject 6, did not finish, 4.16 Based on the table above, enter the 'Weight 1' for the rat that did not finish the race. Enter the value to two decimal places.
4.16
statistic
A calculation derived from samples
A sample can offer us important insights into a population. What is our standard for obtaining a representative sample?
A simple random sample (SRS)
Below are data on the first six rats in the dataset. The variables 'hormone' and 'finished' have been coded as numbers substituting for the possible responses, yes and no. For this study 1='yes' and 0='no'. Subject 1, received hormone, finished Subject 2, received hormone, finished Subject 3, did not receive hormone, finished Subject 4, did not receive hormone, finished Subject 5, did not receive hormone, finished Subject 6, received hormone, did not finish Based on the information provided above, which statement is false?
All of the rats that did receive the hormone finished the maze.
Which of the following would not be considered raw data?
Average age of ballet dancers attending The Juilliard School.
Structured data
Data that has easily identifiable structure such as rows and columns or groups with similar attributes, the top row displays the variables or attributes that were measured during analysis, each row then represents data for a single record
Spice level of salsa at a restaurant (mild, medium, spicy) Length (in seconds) of each song on a Michael Jackson album Names of the top five best-selling books on the New York Times bestsellers list Height of children in a kindergarten class Only one of the following scales of measurement is not represented above. Which is it?
Discrete
By definition, what must be true of a simple random sample?
Every individual in a population has an equal chance of being selected for our sample.
sampling error
Every time we use a sample to estimate something about the population, we will achieve slightly different results, even if we repeat the study exactly using new samples from the same population. The differences in the sample results can lead to differences in the population estimates from study to study. This lack of precision cannot be avoided unless we measure the entire population
Which of the following is an example of numerical data being converted to ordinal data?
Happiness scores (measured on a scale of 1-10) recorded as not happy, happy, and very happy.
convenience sampling
In this method a researcher only includes people who were convenient to obtain a sample from, such as a teacher sampling from just their students to make an inference about a larger population of school children.
A veterinarian doing a study on which type of dog food helps dogs lose the most weight realizes that her scale is miscalibrated and consistently measures things weights 2 pounds less than are.
Instrument bias due to miscalibration
Each student was asked, "Did you play sports in high school?" Their responses were recorded as "1" for YES and "0" for NO. What kind of data do you have now?
It is still categorical data, even though numbers are used to represent categories. Below are examples of data:
Emotional expressions such as anger, sadness, joy, disgust and surprise
Nominal
A professor wants to know how students felt about a new topic they introduced during class. They emailed 15 randomly selected students and asked them to fill out an anonymous survey about the class, but only 5 filled it out.
Nonresponse bias
Do the Lession 1.1 Practice Problems
Okay
Do the Lession 1.2 Practice Problems
Okay
Do the Lesson 1.3 Practice Problems
Okay
State police set up a roadblock on a major highway at 7 am to estimate the percentage of cars with up-to-date registration, insurance and safety inspection stickers. This morning, they find problems with about 10% of the cars they stop.
Under-representation of problems resulting from sampling bias
A question posted on the Lycos Web Site on June 18, 2000 asked visitors to the site to say whether or not they agreed with the statement: "Marijuana should be legally available for medicinal purposes."
Voluntary response bias
parameter
When we complete a calculation on a set of data from a population,
population
a collection of all possible members or outcomes for a group we are interested in, total group being studied
sampling frame
a list of all those within a population who can be sampled
stratified random sampling
a population is divided into smaller groups or clusters (for example: freshmen, sophomores, etc.) and then samples are randomly selected from each cluster
simple random sampling
a sampling method where each member of the population has an exactly equal chance of being selected
sample
a smaller group from the population that represents the population well, a representative part of the population
judgmental sampling
a type of non-random sample that is selected based on the opinion of an expert
A particular population of laboratory rats reach an average weight of 510 grams at age 6 months. To test the effectiveness of a new growth hormone, a researcher selects a sample of 10 newborn rats and injects each rat with the hormone. Six months later, the rats in the sample are weighed and the researcher finds an average weight of 528 grams. The lab assistant forgot to record the weight of each lab rat, and instead only listed their weights as: underweight, standard weight, or overweight. What information has been lost with this change of measurement scale? Select all correct answers.
a. The ability to rank order (i.e. smallest to largest) the weight of each the rats b. The magnitude of the weight difference between any two mice c. The ability to calculate the average weight of the sample
A researcher is interested in the relationship between time of day of departure and if a flight was delayed or not. She collected information on 120 flights by selecting 40 flights that were scheduled to depart in the morning (before 11 am), 40 flights in the afternoon (11 am - 4 pm), and 40 flights in the evening (after 4 pm). If a flight left more than 5 minutes after the original departure time, she marked the flight as delayed. Which are the variable(s) of interest in this study? Select all the correct answers.
a. Whether a flight was delayed or not b. The time of day the flight left
A researcher is interested in the relationship between recall and the number of syllables in a word in adults in the US. She prepares three lists of 40 words. One list contains all one-syllable words; another has only two-syllable words; and the final list consists of all three-syllable words. She gives 75 adult research participants 5 minutes to study each list, and then list as many words as they can recall. Which are the variable(s) of interest in this study? Select all the correct answers.
a. number of syllables in each word b. number of words recalled
Scenario 1: Researchers waited outside of a bar they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the bar and asked them, in front of their friends, whether they thought drinking and driving was a serious problem. Match each of the following terms for Scenario 1: population parameter of interest sample statistic
adults of drinking age, proportion of the population that agrees that drinking and driving is a problem, every 10th person leaving the bar, proportion of the sample that agrees that drinking and driving is a problem
Scenario 2: The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances. Match each of the following terms for Scenario 2: population parameter of interest sample inference
all soil surrounding former waste dump, concentration of toxic chemicals in all soil, 16 soil samples, conclusion that there are not elevated levels of chemicals at the dump
Variables
attributes measured in the course of a study
Data
can be any form of information, but what separates it from a random list of numbers or words is knowing the context of that information; individual measurements or observations in context; pieces of information, such as numbers, words, measurements, observations, or descriptions of things in context
Voluntary response bias
can happen when sample responses come from self-selected volunteers (ex. internet surveys).
Instrument bias
can occur as a result of systematically measuring responses inaccurately (ex. improperly calibrated scale)
Under- or over-representation
can occur if we choose to select our sample from a time or place during which certain portions of the population are sampled more or less frequently than they normally would have been.
Questionnaire/interviewer bias
can occur when the way in which a question is asked can alter the participants responses
Discrete variables
can only take on specific values (typically integers) meaning there will be gaps between the possible values we can report. For example: -number of siblings (0, 1, 2, 3) -year of birth (1999, 2000, 2001)
Continuous variables
can take on any real number value (can have decimals). For example: -height (65.4 inches, 1.77 meters) -temperature (98.6 F, 21.2 C, 101 F)
The ethnicity of each student is what kind of variable?
categorical (qualitative) and nominal
Measurement bias
comes from some form of measurement error.
Dosage of medication (in mg) taken by a patient every four hours
continuous
Grade as a percentage on a history exam
continuous
Scenario 3: Dairy inspectors visit dairy farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm reinspected until purity is restored. Match each of the following elements in Scenario 3: population parameter of interest sample statistic
dairy farms, proportion passing inspection at all dairy farms, dairy farms that were visited, proportion of sample of dairy farms passing inspection
Raw data
data that appears in its original form. This can be a list of numbers or words.; A list of numbers, names, letters, colors, etc.
A researcher is interested in the relationship between recall and the number of syllables in a word in adults in the US. She prepares three lists of 40 words. One list contains all one-syllable words; another has only two-syllable words; and the final list consists of all three-syllable words. She gives 75 adult research participants 5 minutes to study each list, and then list as many words as they can recall. What scale of measurement is being used to measure the number of words recalled?
discrete
Number of children a married couple wants to have
discrete
Sampling bias
happens when the sample we choose does not reflect the full spectrum of the population.
Ordinal variables
have an inherent or obvious order. For example: -Likert scales (strongly disagree, disagree, neutral, agree, strongly agree) -class in school (freshman, sophomore, junior, senior)
Nominal variables
have categories with no distinct or defined order; or a difference in name only. Also, variables with only two categories. For example: -gender -attendance (present or absent) -nationality -two category data (yes or no)
Categorical (qualitative) variables
have values that describe labels or attributes. Even if the categories can be placed in a logical order, they have no magnitude or units. There are two major scales for categorical variables
Data Set
information presented in an organized format
Statistics
involves the tools and techniques that allow us to collect, organize, describe, analyze, and ultimately present an interpretation of the data; science of collecting, organizing, analyzing, and interpreting information; the techniques for collecting, organizing, analyzing, and interpreting data
Numerical (quantitative) variables have
magnitude, are measure-able, and units, with values that carry an equal weight. For example, the difference between 1 and 2 on a numeric scale must represent the same difference as between 9 and 10. There are two major scales for numerical variables
The number of computer science majors that are attending freshman orientation is what kind of variable?
numerical (quantitative) and discrete
Small, medium or large size drink at a fast-food restaurant
ordinal
Scenario 2: Some people have been complaining that the children's playground at a local elementary school is too small and is in need of repair. The principal decides to survey parents to see if they believe the playground should be rebuilt. Parents are handed questionnaires when they pick up their children from school. Match each of the following elements in Scenario 2: population parameter of interest sample statistic
parents of children at the elementary school, percentage of parents at the school that agree playground should be rebuilt, parents that returned the survey, percentage of parents who returned the survey that agree the playground should be rebuilt
Nonresponse bias
people selected to participate in the survey do not complete it.
Scenario 1: Some people that race greyhounds believe that giving the dogs large doses of vitamin C will make them run faster. Researchers at the University of Florida tried three different diets in random order on each of five different greyhounds. Surprisingly, when the dogs ate higher amounts of vitamin C, they ran more slowly. Match each of the following elements in Scenario 1: population parameter of interest sample statistic
racing greyhounds, average speed of racing greyhounds, 5 greyhounds, average speed of the 5 greyhounds
A researcher is interested in the relationship between recall and the number of syllables in a word in adults in the US. She prepares three lists of 40 words. One list contains all one-syllable words; another has only two-syllable words; and the final list consists of all three-syllable words. She gives 75 adult research participants 5 minutes to study each list, and then list as many words as they can recall. In the study above: The number of words recalled are the ________.
raw data
Bias can destroy our ability to gain insights from our sample. What are the two primary sources of bias in sampling?
selecting a non-representative sample and measuring improperly
Selection bias
some individuals within a target population are more likely to be selected for inclusion than others.
A researcher is interested in the relationship between recall and the number of syllables in a word in adults in the US. She prepares three lists of 40 words. One list contains all one-syllable words; another has only two-syllable words; and the final list consists of all three-syllable words. She gives 75 adult research participants 5 minutes to study each list, and then list as many words as they can recall. In the study above: The average number of one, two, and three-syllable words recalled are the __________.
statistics
A researcher wanted to investigate the average amount of time it takes his coffee maker to brew coffee in the morning. He measures the time it takes his coffee to finish brewing each morning for 25 days and then takes the average of the times. What is his variable of interest?
the amount of time it takes to brew
A particular population of laboratory rats reach an average weight of 510 grams at age 6 months. To test the effectiveness of a new growth hormone, a researcher selects a sample of 10 newborn rats and injects each rat with the hormone. Six months later, the rats in the sample are weighed and the researcher finds an average weight of 528 grams. Which of the following would not be considered raw data in this study?
the average weight of the sample rats
statistical inference
the process of using a sample statistic to estimate a population parameter, where we attempt to make predictions about the effects of our actions in the world, based on data.
In a structured data set, the top row of information displays...
the variables we measured.
Simply put, learning statistics can help us...
think more clearly about data.
confounding/lurking variables
variable external to study that effects the relationship between study variables
Categorical
variables have value that describe labels or attributes
Continuous
variables that can take on any real number value
Numerical
variables that have magnitude and units with values that carry equal weight
Nominal
variables with categories that have no distinct order
Scenario 3: In a large school system with 25 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test to be promoted to the next grade level. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for information gathering. Match each to the form of bias that is likely to result. Put a big ad in the newspaper and ask people to log in with their opinions to the PTA website. Randomly select one elementary school and call every parent by phone. Send a survey home with every student, and ask parents to fill it in and return it the next day. Randomly select 20 parents from each elementary school and follow up with email or phone, and then personal visit if no response.
voluntary response bias, possible non-representative sample, nonresponse bias, should be unbiased